Abstract
In this paper, a hierarchical sliding mode controller is proposed for a single-link flexible manipulator positioning with active vibration suppression. The derived model is highly nonlinear, and the manipulator is affected by unknown, matched, and bounded model uncertainties and/or external disturbances. First, the dynamic equations of the system are derived using the Hamilton’s principle, and the elastic movement is approximated using the assumed mode method. System equations are then formulated in the state space form and adapted to the control algorithm via suitable decomposition into two interconnected lower-order subsystems associated with the rigid body motion and the flexible one respectively. Next, an integral sliding mode control is proposed to tackle the matched uncertainties and/or disturbances. Lyapunov’s theory has been applied to prove the asymptotic stability of the sliding surface. Simulation results showed that the proposed controller can effectively reduce the residual vibration while positioning the flexible manipulator.
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Appendix
Appendix
1.1 Numerical values of model matrices used for simulation
The Mass Matrix: \(M\left(q\right)=\left[\begin{array}{cc}0.13 +0.2783{q}^{2}& 0.1163\\ 0.1162& 0.2783\end{array}\right]\)
The vector of nonlinear centrifugal and Coriolis terms: \(h\left(q,\dot{q}\right)=\left[\begin{array}{c}0.5566 \quad q\dot{q}\dot{\theta }\\ -0.2783 \quad q{\dot{\theta }}^{2}\end{array}\right]\)
The stiffness matrix: \(K\left(q\right)=\left[\begin{array}{cc}0& 0\\ 0& 22.94\end{array}\right]\)
1.2 Simulink model/control system diagram
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Ben Tarla, L., Bakhti, M. & Bououlid Idrissi, B. Robustifying hierarchical sliding mode control for active vibration suppression of a flexible manipulator using integral sliding mode control. Int J Intell Robot Appl 7, 641–651 (2023). https://doi.org/10.1007/s41315-023-00289-9
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DOI: https://doi.org/10.1007/s41315-023-00289-9